While plastic is certainly no slice of cherry pie, it has one thing going for it that paper does not: relative strength. Paper falls apart really easily. All you need to do is put one jug of milk in a paper bag and experience The Great Bottom Falling Out Phenomenon to know that paper bags aren’t a cure-all.
In some ways, this makes paper more disposable than plastic. And while plastic can be washed if it gets yucky, paper is done for as soon as food or oil soak into its fibers. Once that happens, you can’t even recycle it. Considering the fact that “It’s recyclable!” is often cited as the main argument in favor of paper, that’s pretty bad news.
If you must choose paper, at least try to keep wet items out of it and don’t overfill it. That way it won’t tear, and hopefully you can use it again. Even when you can, though, paper only stands up to a use or three. Wholesale reusable grocery bags, on the other hand, keep trucking long afterward, good for hundreds or even thousands of uses.